cytoscape/src/collection/algorithms/karger-stein.mjs

Graph theory (a.k.a. network) library for analysis and visualisation

import { error } from '../../util/index.mjs';

const sqrt2 = Math.sqrt(2);

// Function which colapses 2 (meta) nodes into one
// Updates the remaining edge lists
// Receives as a paramater the edge which causes the collapse
const collapse = function( edgeIndex, nodeMap, remainingEdges ){
  if( remainingEdges.length === 0 ){
    error(`Karger-Stein must be run on a connected (sub)graph`);
  }

  let edgeInfo = remainingEdges[ edgeIndex ];
  let sourceIn = edgeInfo[1];
  let targetIn = edgeInfo[2];
  let partition1 = nodeMap[ sourceIn ];
  let partition2 = nodeMap[ targetIn ];
  let newEdges = remainingEdges; // re-use array

  // Delete all edges between partition1 and partition2
  for( let i = newEdges.length - 1; i >=0; i-- ){
    let edge = newEdges[i];
    let src = edge[1];
    let tgt = edge[2];

    if(
      ( nodeMap[ src ] === partition1 && nodeMap[ tgt ] === partition2 ) ||
      ( nodeMap[ src ] === partition2 && nodeMap[ tgt ] === partition1 )
    ){
      newEdges.splice(i, 1);
    }
  }

  // All edges pointing to partition2 should now point to partition1
  for( let i = 0; i < newEdges.length; i++ ){
    let edge = newEdges[i];

    if( edge[1] === partition2 ){ // Check source
      newEdges[i] = edge.slice(); // copy
      newEdges[i][1] = partition1;
    } else if( edge[2] === partition2 ){ // Check target
      newEdges[i] = edge.slice(); // copy
      newEdges[i][2] = partition1;
    }
  }

  // Move all nodes from partition2 to partition1
  for( let i = 0; i < nodeMap.length; i++ ){
    if( nodeMap[i] === partition2 ){
      nodeMap[i] = partition1;
    }
  }

  return newEdges;
};

// Contracts a graph until we reach a certain number of meta nodes
const contractUntil = function( metaNodeMap, remainingEdges, size, sizeLimit ){
  while( size > sizeLimit ){
    // Choose an edge randomly
    let edgeIndex = Math.floor( (Math.random() * remainingEdges.length) );

    // Collapse graph based on edge
    remainingEdges = collapse( edgeIndex, metaNodeMap, remainingEdges );

    size--;
  }

  return remainingEdges;
};

const elesfn = ({

  // Computes the minimum cut of an undirected graph
  // Returns the correct answer with high probability
  kargerStein: function(){
    let { nodes, edges } = this.byGroup();
    edges.unmergeBy(edge => edge.isLoop());

    let numNodes = nodes.length;
    let numEdges = edges.length;
    let numIter = Math.ceil( Math.pow( Math.log( numNodes ) / Math.LN2, 2 ) );
    let stopSize = Math.floor( numNodes / sqrt2 );

    if( numNodes < 2 ){
      error( 'At least 2 nodes are required for Karger-Stein algorithm' );
      return undefined;
    }

    // Now store edge destination as indexes
    // Format for each edge (edge index, source node index, target node index)
    let edgeIndexes = [];
    for( let i = 0; i < numEdges; i++ ){
      let e = edges[ i ];
      edgeIndexes.push([ i, nodes.indexOf(e.source()), nodes.indexOf(e.target()) ]);
    }

    // We will store the best cut found here
    let minCutSize = Infinity;
    let minCutEdgeIndexes = [];
    let minCutNodeMap = new Array(numNodes);

    // Initial meta node partition
    let metaNodeMap = new Array(numNodes);
    let metaNodeMap2 = new Array(numNodes);

    let copyNodesMap = (from, to) => {
      for( let i = 0; i < numNodes; i++ ){
        to[i] = from[i];
      }
    };

    // Main loop
    for( let iter = 0; iter <= numIter; iter++ ){
      // Reset meta node partition
      for( let i = 0; i < numNodes; i++ ){ metaNodeMap[i] = i; }

      // Contract until stop point (stopSize nodes)
      let edgesState = contractUntil( metaNodeMap, edgeIndexes.slice(), numNodes, stopSize );
      let edgesState2 = edgesState.slice(); // copy

      // Create a copy of the colapsed nodes state
      copyNodesMap(metaNodeMap, metaNodeMap2);

      // Run 2 iterations starting in the stop state
      let res1 = contractUntil( metaNodeMap, edgesState, stopSize, 2 );
      let res2 = contractUntil( metaNodeMap2, edgesState2, stopSize, 2 );

      // Is any of the 2 results the best cut so far?
      if( res1.length <= res2.length && res1.length < minCutSize ){
        minCutSize = res1.length;
        minCutEdgeIndexes = res1;
        copyNodesMap(metaNodeMap, minCutNodeMap);
      } else if( res2.length <= res1.length && res2.length < minCutSize ){
        minCutSize = res2.length;
        minCutEdgeIndexes = res2;
        copyNodesMap(metaNodeMap2, minCutNodeMap);
      }
    } // end of main loop


    // Construct result
    let cut = this.spawn( minCutEdgeIndexes.map(e => edges[e[0]]) );
    let partition1 = this.spawn();
    let partition2 = this.spawn();

    // traverse metaNodeMap for best cut
    let witnessNodePartition = minCutNodeMap[0];
    for( let i = 0; i < minCutNodeMap.length; i++ ){
      let partitionId = minCutNodeMap[i];
      let node = nodes[i];

      if( partitionId === witnessNodePartition ){
        partition1.merge( node );
      } else {
        partition2.merge( node );
      }
    }

    // construct components corresponding to each disjoint subset of nodes
    const constructComponent = (subset) => {
      const component = this.spawn();

      subset.forEach(node => {
        component.merge(node);

        node.connectedEdges().forEach(edge => {
          // ensure edge is within calling collection and edge is not in cut
          if (this.contains(edge) && !cut.contains(edge)) {
            component.merge(edge);
          }
        });
      });

      return component;
    };

    const components = [
      constructComponent(partition1),
      constructComponent(partition2)
    ];

    let ret = {
      cut,
      components,

      // n.b. partitions are included to be compatible with the old api spec
      // (could be removed in a future major version)
      partition1,
      partition2
    };

    return ret;
  }
}); // elesfn


export default elesfn;